Today the bulk of goods shipped from international destinations to the United States (U.S.) arrive in steel cargo containers. The vast majority of these containers comes in one of two common varieties: 8′ by 8′ by 20′, i.e., one Twenty-foot Equivalent Unit (TEU); and 8′ by 8′ by 40′, i.e., two TEUs. Over forty million TEUs arrive in the U.S. in each year. One of the primary missions of U.S. Customs Service has been the inspection of these cargo containers for manifest verification and contraband detection. The heightened threat of weapons of mass destruction (WMD) being transported through this shipping modality has resulted in a significant interest in methods of insuring the integrity of the containers from offshore manufacture or shipper to its U.S. destination. Sealing the container alone is not sufficient to insure the integrity of the shipping container contents. Studies show that the most sophisticated sealing mechanism remains defeatable by those whose mission it is to affect the contents of the container. In addition, volume alone makes detailed individual inspection of each container resource-intensive if not infeasible. National security issues drive an increasing level of vigilance to reduce the risk of admitting s contents into the country.
One approach to managing the security concerns associated with allowing containers to enter the U.S., without detailed individual inspection upon arrival, is to have a trusted shipper or an Independent Goods Inspector (IGI) inspect the container when the cargo is loaded. After inspection and loading, the container is sealed. Subsequently, those containers bearing seals that show signs of tampering can be selected for detailed individual inspection. The use of seals, while potentially effective to indicate tampering through the container door, does not address tampering through other methods, e.g., entry through the sides or ends of the container.
A pulse of energy introduced into a hollow conductive box will cause the box to respond at its resonant frequencies. Such a box can be visualized as a waveguide shorted at each end. Such a waveguide can support a stationary wave pattern of only those resonant modes whose frequencies lead to an integral number of half-wavelengths between opposite conductive walls of the waveguide. A rectangular waveguide of dimensions a×b×d has resonant frequencies at fmnq given in Equation 1—where m, n, and q are integers describing the number of half-wavelengths between the a, b, and d walls respectively. The integers in m, n, and q collectively represent a mode of the resonant response whose frequency is:
                              f          mnq                =                              c                          2              ⁢                                                          ⁢              π              ⁢                                                                    μ                    R                                    ⁢                                      ɛ                    R                                                                                ⁢                                                                      (                                                            m                      ⁢                                                                                          ⁢                      π                                        a                                    )                                2                            +                                                (                                                            n                      ⁢                                                                                          ⁢                      π                                        b                                    )                                2                            +                                                (                                                            q                      ⁢                                                                                          ⁢                      π                                        d                                    )                                2                                                                        (        1        )            
In Equation 1, c is the velocity of light while ∈R and μR are the relative electrical permittivity magnetic permeability of the dielectric media—nominally air, in which case ∈R=μR=1.
The quality factor, Q, is a common parameter used to describe the relative “strength” of any particular resonant mode and is defined as the energy stored in the system divided by the energy lost per radio frequency (RF) cycle. The Q is also equal to the resonant frequency divided by the bandwidth at the half-power points of the response curve. The larger the Q-value, the higher the peak response of the resonance and the narrower its width. An infinite Q-value would correspond to a mode with infinite response and zero bandwidth. In our example rectangular cavity with dimensions a×b×d, the Q of the lowest frequency Transverse Electric (TE) mode {m=1, n=0, q=1} can be expressed as:
                              Q          101                =                                                                              (                  kad                  )                                3                            ⁢              b              ⁢                                                          ⁢              η                                      2              ⁢                                                          ⁢                              π                2                            ⁢                              R                s                                              ⁢                      1                          (                                                2                  ⁢                                                                          ⁢                                      a                    3                                    ⁢                  b                                +                                  2                  ⁢                                      bd                    3                                                  +                                                      a                    3                                    ⁢                  d                                +                                  ad                  3                                            )                                                          (        2        )            where k=2π/λ (λ is the wavelength), η2=μ/∈=μoμR/∈o∈R, and RS is the surface resistivity of the metal walls of the waveguide. The higher the Q, the greater the system response to a stimulus and the more easily that response is to identify compared with background electronic noise.
FIG. 1 is a plot of the theoretical modes of a one TEU equivalent copper waveguide. The individual curves are labeled with their m and n mode numbers respectively, and are shown as a function he longitudinal mode number q. Because the waveguide has a square cross-section, the plots produced by switching m and n are equivalent (e.g. the horizontal and vertical modes are degenerate in frequency). The observable mode structure of an empty container would be the projection of the “dots” in FIG. 1 onto the vertical axis—a large number of overlapping resonant modes.